What is the solution for x^2(dy)/(dx)=y^2,y(1)=-1 ?

The solution for x^2(dy)/(dx)=y^2,y(1)=-1 is y=-x/(-1+2x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

x^2(dy)/(dx)=y^2,y(1)=-1

x^{2} \frac{d y}{d x} = y^{2}, y (1) = - 1

y = - \frac{x}{- 1 + 2 x}

Solution steps

x^{2} \frac{d y}{d x} = y^{2}

Solve separable ODE:

y = - \frac{x}{- 1 + 2 x}

y = - \frac{x}{- 1 + 2 x}

\frac{x}{2} cot (y) \frac{d y}{d x} = - 1

4 x y^{2} d x + (x^{2} + 1) d y = 0

\frac{d y}{d x} = - \frac{6}{8} x^{4} y^{6}

tan (x) sin^{2} (y) d x + cos^{2} (x) cos (y) d y = 0

\frac{d y}{d x} = \frac{4 x}{7 y}

What is the solution for x^2(dy)/(dx)=y^2,y(1)=-1 ?
The solution for x^2(dy)/(dx)=y^2,y(1)=-1 is y=-x/(-1+2x)